Question: Simplify the following expression: $ r = \dfrac{-4}{7} + \dfrac{4t}{t + 7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{t + 7}{t + 7}$ $ \dfrac{-4}{7} \times \dfrac{t + 7}{t + 7} = \dfrac{-4t - 28}{7t + 49} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{4t}{t + 7} \times \dfrac{7}{7} = \dfrac{28t}{7t + 49} $ Therefore $ r = \dfrac{-4t - 28}{7t + 49} + \dfrac{28t}{7t + 49} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-4t - 28 + 28t}{7t + 49} $ $r = \dfrac{24t - 28}{7t + 49}$